Few scrappy methods for market research:
1. Internal data: Analyze internal customer service data if available (type of customers who frequently call for support). Alternatively, perform a quick 1-2 week observation study of in-store traffic.
2. Web Traffic Insights: Analyze online visitors. Implement a web analytics platform now if it already does not exist. Google Analytics is easy to begin with and gives decent demographic data (geo/gender/age). You’ll get richer user data if you integrate ‘Log in with Facebook’ (via Janrain etc.).
3. Social Analytics: Does company have a FB/Twitter page? If yes, there are tools like Microstrategy Wisdom that can provide an overview of fan/follower segments.
4. Social Listening: Listen for your brand or product in general, & run demographics report on this volume. While this may not give an exact picture of the current customers but will include posts from potential/current/ex customers. Due to lack of budget you may want just a trial license of social listening platform such as Radian6/ NetBase. Note that, Twitter firehose access that comes at a cost.
5. Competitive study: Check out Google Trends, Google Keyword Tool or customer reports (consumerreports.org) for similar competitors or the industry itself.
Finally, you can just show up in shopping mall and interview shoppers, or just an observation study.